1. Field of the Invention
The present invention relates to a filter device and an electronic musical instrument equipped with the filter device.
2. Description of the Related Art
Tone color of an acoustic musical instrument is changed according to change of the amplitude ratio of a harmonic tone in relation to a fundamental tone. In particular, when tone color is changed according to strong and weak of performance, as a musical instrument is performed strongly (for example, a piano key is touched strongly), the amplitude ratio of a high order harmonic tone becomes higher. Meanwhile, as the musical instrument is performed weakly (for example, the piano key is touched weakly), the amplitude ratio of the high order harmonic tone becomes smaller.
FIG. 12A and FIG. 12B are graphs showing waveforms of an acoustic piano. FIG. 12A shows a waveform when the piano key is touched fortissimo, and FIG. 12B shows a waveform when the piano key is touched mezzo piano. FIG. 13A and FIG. 13B are graphs showing spectrums calculated based on the respective waveforms of FIG. 12A and FIG. 12B. In FIG. 13A and FIG. 13B, the horizontal axis (frequency axis) is linear, and the vertical axis is shown in units of dB. The spectrums of FIG. 13A and FIG. 13B are calculated based on the processing that sample 4096 is cut out from the section in the vicinity of sounding start of the waveforms shown in FIG. 12A and FIG. 12B, with the use of Blackmann's window function.
FIG. 14 is a diagram showing spectrum envelopes extracted from the spectrums shown in FIG. 13A and FIG. 13B. As shown in FIG. 14, the spectrum envelopes have approximately constant slopes from the fundamental wave to the higher harmonic wave, and the slopes are uniformly changed according to strength of the performance. In the example of FIG. 14, as the strength of the performance becomes stronger, the slopes become larger (that is, approaches 0). Therefore, when color tones are changed by a filter circuit in an electronic musical instrument, the filter circuit desirably has the filter characteristics with the spectrum envelopes as shown in FIG. 14.
The existing filter transfer function is shown in the following Formula 1.
      Formula    ⁢                  ⁢    1                                            H            ⁡                          (              z              )                                =                                    w              0              2                                      1              +                                                (                                                            -                      2                                        +                                          w                      0                      2                                        +                                                                  w                        0                                            ⁢                      Q                                                        )                                ⁢                                  z                                      -                    1                                                              +                                                (                                      1                    -                                                                  w                        0                                            ⁢                      Q                                                        )                                ⁢                                  z                                      -                    2                                                                                                            (          1          )                    
where ω0=2 pfc/fs (0<ω0<1)
where fc represents a cutoff frequency, fs represents a sampling frequency, ω0 represents a cutoff angle frequency, and Q represents selectivity.
In the existing filter circuit, the filter characteristics are changed according to ω0 (or fc) and Q. Therefore, the filter circuit uses ω0 (or fc) and Q as parameters, and the characteristics are changed based on these parameters.
FIG. 15 is a graph showing filter characteristics when fc as a parameter is changed in a secondary IIR filter having the characteristics shown in Formula 1. In FIG. 15, the horizontal axis (frequency axis) is linear (0 to 10 kHz), and the vertical axis is shown in units of dB. As shown in FIG. 15, even when fc is changed, the changed filter characteristics are far from the characteristics as shown in FIG. 13A, FIG. 13B, and FIG. 14. Therefore, in the electronic musical instrument, there has been a problem that it is extremely difficult to realize tone color change equal to the tone color change of the acoustic piano by controlling the cutoff frequency.
Further, currently, many electronic musical instruments employ the PCM method. In the PCM method, an attack-time waveform when musical sound is generated (attack time) and waveform data of the subsequent repetition waveform are stored in the waveform memory. On and after the attack time, the waveform data of the repetition waveform is repeatedly read, and thereby the capacity of the waveform memory is decreased. However, when only the same waveform is repeated, the color tones are fixed and monotonized. Therefore, the tone colors are changed as time goes on by the filter circuit. In particular, in an acoustic piano, the higher order harmonic tone is more fastly attenuated as time goes on. It has not been possible to realize such a change by the existing filter circuit.
For example, in Japanese Laid-Open (Kokai) Patent Publication No. 4-78213, a filter using a specific frequency f0 in which the transfer characteristics start to change and the change ratio thereof as a parameter instead of the cutoff frequency fc is suggested. However, even when the filter disclosed in the foregoing patent document is used, it has been particularly difficult to realize change equal to the tone color change of an acoustic piano. In particular, there has been the following problem. That is, the frequency in which the maximum attenuation level or the maximum enhancement level of a given frequency is changed to a given ratio thereof (hereinafter referred to as “turnover frequency” in the specification) is moved according to change of the parameter.